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If I have a Conduit of Ruin on the battlefield and say that I will be casting Endless One for 10 mana, will the cost reduction of 2 mana from the Conduit of Ruin's effect reduce the X so that the Endless One is 8/8 or will it remain 10/10?

My thinking is going with X = 10, but I need to make sure.

Then, expanding on that:

If I have 4 x Conduit of Ruin on the battlefield, could I cast an 8/8 Endless One for "free", using only the total cost reduction of 8 mana (from the 4 x Conduit of Ruins) as the "X" casting cost?

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    You might think of it like this (summarizing the answers, which is why I put it as a comment which can be temporary): Conduit changes the cost, it doesn't change the X. – David Z Dec 5 '15 at 16:30
  • Your first and second example process the cards differently. If you reduced X from the amount of mana you want to pay for each Conduit like you did in the first example it would be a -8. The Conduit allows you to increase X without spending more mana, not decrease it from the amount spent. So for 10 mana you can get a 12/12 not an 8/8. – Fr33dan Dec 6 '15 at 0:28
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Yes, your interpretation is correct. From the card rulings:

Conduit of Ruin’s last ability doesn’t change the mana cost or converted mana cost of any spell. It changes only the total cost you actually pay.

If you control more than one Conduit of Ruin, the last ability of each of them applies only to the first creature spell you cast each turn, not to different spells; if you control two Conduits of Ruin, the first creature spell you cast each turn will cost {4} less.

If the first creature spell you cast in a turn has {X} in its mana cost, you choose the value of X before calculating the spell’s total cost. For example, if the first creature spell you cast in a turn has a mana cost of {X}{G}, you could choose 2 as the value of X and pay {G} to cast the spell.

So, the value that you pick for X is fixed, the only thing that changes is what you actually pay.

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You choose a value for X which is then reduced by two colourless mana for each conduit you have on the battlefield.

If I have a Conduit of Ruin on the battlefield and say that I will be casting Endless One for 10 mana, will the cost reduction of 2 mana from the Conduit's effect reduce the X so that the Endless one is 8/8 or will it remain 10/10?

You choose a value for X and then a slew of effects may either increase or decrease the cost. Here is the pertinent rules. It is a bit long but worth the read.

601.2a To propose the casting of a spell, a player first moves that card (or that copy of a card) from where it is to the stack. It becomes the topmost object on the stack. It has all the characteristics of the card (or the copy of a card) associated with it, and that player becomes its controller. The spell remains on the stack until it’s countered, it resolves, or an effect moves it elsewhere.

601.2b If the spell is modal, the player announces the mode choice (see rule 700.2). If the player wishes to splice any cards onto the spell (see rule 702.46), he or she reveals those cards in his or her hand. If the spell has alternative or additional costs that will be paid as it’s being cast such as buyback or kicker costs (see rules 117.8 and 117.9), the player announces his or her intentions to pay any or all of those costs (see rule 601.2f). A player can’t apply two alternative methods of casting or two alternative costs to a single spell. If the spell has a variable cost that will be paid as it’s being cast (such as an {X} in its mana cost; see rule 107.3), the player announces the value of that variable. If a cost that will be paid as the spell is being cast includes hybrid mana symbols, the player announces the nonhybrid equivalent cost he or she intends to pay. If a cost that will be paid as the spell is being cast includes Phyrexian mana symbols, the player announces whether he or she intends to pay 2 life or the corresponding colored mana cost for each of those symbols. Previously made choices (such as choosing to cast a spell with flashback from a graveyard or choosing to cast a creature with morph face down) may restrict the player’s options when making these choices.

601.2f The player determines the total cost of the spell. Usually this is just the mana cost. Some spells have additional or alternative costs. Some effects may increase or reduce the cost to pay, or may provide other alternative costs. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on. The total cost is the mana cost or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions. If multiple cost reductions apply, the player may apply them in any order. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be {0}. It can’t be reduced to less than {0}. Once the total cost is determined, any effects that directly affect the total cost are applied. Then the resulting total cost becomes “locked in.” If effects would change the total cost after this time, they have no effect.

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    I think it would improve this answer to specifically say that the value of X is not reduced by the cost reduction mechanisms. Also, you posted 3 large paragraphs of rules quotations and bolded half a sentence (and that half doesn't really say anything alone). I would suggest emphasizing all of the parts that you think are relevant and/or skipping the parts that are irrelevant. – murgatroid99 Dec 4 '15 at 18:37

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